Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 3
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dzik, W. Jarvinen, J. and Kondo, M. 2014. Characterizing intermediate tense logics in terms of Galois connections. Logic Journal of IGPL, Vol. 22, Issue. 6, p. 992.


    Dyckhoff, Roy Sadrzadeh, Mehrnoosh and Truffaut, Julien 2012. Algebra, Proof Theory and Applications for a Logic of Propositions, Actions and Adjoint Modal Operators. Electronic Notes in Theoretical Computer Science, Vol. 286, p. 157.


    Gore, Rajeev Postniece, Linda Tiu, Alwen and Giese, Martin 2011. On the Correspondence between Display Postulates and Deep Inference in Nested Sequent Calculi for Tense Logics. Logical Methods in Computer Science, Vol. 7, Issue. 2,


    ×

POSITIVE LOGIC WITH ADJOINT MODALITIES: PROOF THEORY, SEMANTICS, AND REASONING ABOUT INFORMATION

  • MEHRNOOSH SADRZADEH (a1) and ROY DYCKHOFF (a2)
  • DOI: http://dx.doi.org/10.1017/S1755020310000134
  • Published online: 01 August 2010
Abstract

We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of “nested” or “tree-sequent” calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.

Copyright
Corresponding author
*OXFORD UNIVERSITY COMPUTING LABORATORY, OXFORD, UK. E-mail:mehrs@comlab.ox.ac.uk
SCHOOL OF COMPUTER SCIENCE, ST ANDREWS UNIVERSITY, ST ANDREWS, SCOTLAND, UK. E-mail:rd@st-andrews.ac.uk
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

A. Baltag , B. Coecke , & M. Sadrzadeh (2007). Epistemic actions as resources. Journal of Logic and Computation, 17, 555585.

A. Baltag , & L. Moss (2004). Logics for epistemic programs. Synthese, 139, 165224.

S. Celani , & R. Jansana (1999). Priestley duality, a Sahlqvist theorem and a Goldblatt-Thomason theorem for positive modal logic. Logic Journal of the IGPL, 7, 683715.

M. Dunn (2005). Positive modal logic. Studia Logica, 55, 301317.

M. Gehrke , H. Nagahashi , & Y. Venema (2005). A Sahlqvist theorem for distributive modal logic. Annals of Pure and Applied Logic, 131, 65102.

R. Goré (1998). Substructural logics on display. Logic Journal of the IGPL, 6(3), 451504.

R. Kashima (1994). Cut-free sequent calculi for some tense logics. Studia Logica, 53, 119135.

M. Moortgat (1995). Multimodal linguistic inference. Logic Journal of the IGPL, 3, 371401.

S. Negri (2005). Proof analysis in modal logic. Journal of Philosophical Logic, 34, 507544.

S. Richards , & M. Sadrzadeh (2009). Aximo: Automated axiomatic reasoning for information update. Electronic Notes in Theoretical Computer Science, 231, 211225.

M. Sadrzadeh (2009). Ockham’s razor and reasoning about information flow. Synthese, 167, 391408.

M. Sadrzadeh , & R. Dyckhoff (2009). Positive logic with adjoint modalities: Proof theory, semantics and reasoning about information. Electronic Notes in Theoretical Computer Science, 249, 451470.

B. von Karger (1998). Temporal algebras. Mathematical Structures in Computer Science, 8, 277320.

H. Wansing (1994). Sequent calculi for normal modal propositional logics. Journal of Logic and Computation, 4(2), 125142.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×